Porous boron-doped diamond composite thin film temperature sensor and method of making same

Abstract

The application discloses a porous boron-doped diamond composite film temperature sensor and a preparation method thereof, and belongs to the field of temperature sensors.The application solves the problems that a traditional boron-doped diamond temperature sensor cannot weaken the phonon-electron coupling phenomenon, the conductivity of the boron-doped diamond temperature sensor has poor sensitivity to temperature change, and an ordinary mechanical assembly mode is easy to be damaged and has an interface thermal adaptation problem.The application sets a micro-nano scale aperture structure arranged in a dot matrix on a boron-doped diamond film, the micro-nano scale aperture structure can make the phonon transport process in the boron-doped diamond occur phonon coherence, weaken the interaction between phonons and electrons, enhance the transport capacity of the electrons, increase the electrical properties of the boron-doped diamond and the temperature sensitivity thereof, on the other hand, a composite film structure formed by the multilayer film is deposited on the surface of a temperature measuring object, mechanical structure stability in a harsh environment is ensured, and temperature measurement errors and delays caused by the interface thermal adaptation can be reduced.The application is mainly used for temperature measurement.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of temperature sensors, and particularly relates to a preparation method of a porous boron-doped diamond composite film temperature sensor applied to extreme fields such as precision machining, geological drilling, spaceflight and space exploration. BACKGROUND

[0002] Temperature is one of the important parameters in various industrial processes and experimental researches, and a temperature sensor is a commonly used sensor device for measuring and monitoring temperature changes in the environment. Traditional temperature sensors usually measure temperature based on non-contact infrared measurement and contact thermocouple measurement, but infrared measurement is not accurate enough, has a large error under cooling conditions, and is easily blocked; contact metal thermocouples usually need to be embedded inside the test workpiece, which not only is too far from the heat source to obtain accurate transient temperature values, but also causes a decrease in strength due to secondary processing of the test workpiece, and the point-to-surface assembly method using insulating glue has greater error and thermal conduction delay. Moreover, metal thermocouples have a series of limitations and deficiencies in extreme environments such as scratching and collision, strong corrosion, space radiation, and are prone to damage and have a short service life. Therefore, developing a temperature sensor with high sensitivity, high precision, high stability and high environmental adaptability has become a research hotspot.

[0003] Diamond is a material with excellent thermal conductivity and chemical stability, sp 3 Bonded carbon atoms make it have excellent mechanical properties, electrical properties, corrosion resistance and radiation resistance. Boron can be doped into the diamond lattice as an acceptor impurity atom to make it a p-type semiconductor with hole conduction. Since the activation energy of the boron atom impurity level is relatively high, about 0.37 eV, in the lower doping range of 10 16 cm -3 ~ 10 19 cm -3 , the activated carrier concentration is greatly affected by temperature, and the lower the doping concentration, the more sensitive the conductivity to temperature. For example, when the boron doping concentration is 4x10 18 cm -3 , the conductivity almost linearly increases in the low temperature range of 0.1K~10K as the temperature rises from 100K to 250K; when the boron doping concentration is 2x10 16 cm -3 , the conductivity rapidly increases in the range of 200K~400K.

[0004] Patent CN201721324913.4 gives a full-depth temperature sensor based on diamond film, but the assembly and packaging of the temperature response element boron-doped diamond film are simple mechanical assembly, which is easy to be damaged by external mechanical vibration and pressure, and the mechanical assembly method has interface thermal adaptation, which will cause temperature measurement error and delay, and the preparation cost of millimeter-level boron-doped diamond film is high. Patent CN202310394227.8 gives a diamond tool with self-sensing cutting force and cutting temperature and a manufacturing method thereof, which uses ion implantation to locally change single crystal diamond into boron-doped diamond with thermal sensitivity, but the cost of single crystal diamond and ion implantation is extremely high, and the anisotropy of single crystal diamond is not suitable for downhole drilling. In addition, due to the existence of obvious phonon-electron coupling phenomenon in the above two schemes, the thermal transport of phonon will interfere with the electrical transport of electron, and the traditional boron-doped diamond temperature sensor cannot weaken the phonon-electron coupling phenomenon, resulting in poor sensitivity of the electrical conductivity of the traditional boron-doped diamond temperature sensor to temperature change. The above problems need to be solved. SUMMARY

[0005] The purpose of the present application is to solve the problems that the traditional boron-doped diamond temperature sensor cannot weaken the phonon-electron coupling phenomenon, resulting in poor sensitivity of the electrical conductivity of the boron-doped diamond temperature sensor to temperature change, and the ordinary mechanical assembly method is easy to damage and has interface thermal adaptation, and the present application provides a porous boron-doped diamond composite film temperature sensor preparation method.

[0006] The porous boron-doped diamond composite film temperature sensor preparation method comprises the following steps:

[0007] A transition layer and an intrinsic diamond film, a periodically arranged mask are sequentially deposited on a temperature measuring workpiece by a chemical vapor deposition method; a boron-doped diamond film with a porous structure is selectively grown on the intrinsic diamond film, then an intrinsic diamond film is deposited on the boron-doped diamond film with a porous structure, and a contact electrode and a lead wire are installed, i.e. the porous boron-doped diamond composite film temperature sensor preparation is completed; the boron-doped diamond film with a porous structure is a boron-doped diamond film with a periodically arranged micro-nano scale pore structure.

[0008] Preferably, the periodically arranged micro-nano scale pore structure in the boron-doped diamond film with a porous structure is composed of an array of holes, or is spliced by a plurality of different periodic units, each periodic unit being composed of an array of holes.

[0009] Preferably, the cross section of the micro-nano scale hole is rectangular, circular or triangular.

[0010] Preferably, the boron-doped diamond film with a porous structure is obtained by selective growth of conductive boron-doped diamond on an intrinsic diamond film.

[0011] Preferably, the boron-doped diamond film with a porous structure has a thickness of 5-500 microns and a boron-doping concentration of 10 16 cm -3 -10 19 cm -3 .

[0012] Preferably, the chemical vapor deposition is magnetron sputtering, electron beam evaporation or metal organic chemical vapor deposition.

[0013] Preferably, the intrinsic diamond film has a thickness of 5-500 microns.

[0014] Preferably, if the temperature-measuring workpiece material is diamond, a transition layer does not need to be deposited.

[0015] Preferably, the mounting leads are connected to the two contact electrodes by using conductive silver paste and then cured.

[0016] A thin-film temperature sensor is obtained by the method for preparing the porous boron-doped diamond composite thin-film temperature sensor.

[0017] The present application has the following beneficial effects:

[0018] The present application uses the thermal sensitivity of boron-doped diamond conductivity to design a method for preparing a porous boron-doped diamond composite thin-film temperature sensor, which has high precision and high stability.

[0019] In addition, a micron-level composite thin-film structure is deposited on the surface of the temperature-measuring object, and the chemical bonding has ultra-high bonding strength, which can ensure the mechanical stability of the structure in harsh environments and reduce the temperature measurement error and delay caused by interface thermal adaptation. The thin-film structure has very small thermal bonding area and thermal capacity, so a large number of thermal probe arrays can be integrated at the heat source position, and the electrical signal is led out by the compensation line at the back end, which has the advantages of high precision, fast response, small damage to the temperature-measuring material, etc. Compared with a thermocouple which is also a contact type but needs to be embedded in the workpiece, the present application can avoid damage to the workpiece. Moreover, the outermost intrinsic diamond film has the functions of encapsulation and insulation protection, as well as the environmental adaptability of scratch and collision resistance, corrosion resistance and radiation resistance.

[0020] The application can meet the contact temperature measurement demand in extreme environment such as high temperature, high pressure, dynamic wear and the like by virtue of the excellent stability of diamond. BRIEF DESCRIPTION OF DRAWINGS

[0021] Figure 1 is a schematic diagram of a porous boron-doped diamond composite thin film temperature sensor structure according to the application;

[0022] Figure 2 is a schematic diagram of the structure of the porous boron-doped diamond film 5;

[0023] Figure 3 is a schematic diagram of the principle of the application of the prepared porous boron-doped diamond composite thin film temperature sensor in combination with a temperature sensing system;

[0024] Figure 4 is a schematic diagram of the overall structure of geological drilling and the overall structure formed by the prepared porous boron-doped diamond composite thin film temperature sensor thereon;

[0025] Figure 5 is a schematic diagram of the circuit principle of the assembly of the porous boron-doped diamond composite thin film temperature sensor in a temperature control switch device;

[0026] In the drawings, reference numeral 1 is a temperature measurement workpiece, reference numeral 2 is a transition layer, reference numeral 3 is an intrinsic diamond film, reference numeral 4 is a mask, reference numeral 5 is a boron-doped diamond film, reference numeral 6 is a micro-nano scale hole, reference numeral 7 is a contact electrode, reference numeral 8 is a lead wire, reference numeral 9 is a drill rod, reference numeral 10 is a power supply, reference numeral 11 is a signal acquisition unit, and reference numeral 12 is a heat dissipation device. DETAILED DESCRIPTION

[0027] The technical solutions in the embodiments of the application will be apparently and completely described below with reference to the drawings in the embodiments of the application. Obviously, the described embodiments are only part of the embodiments of the application, rather than all the embodiments of the application. Based on the embodiments in the application, all other embodiments obtained by a person of ordinary skill in the art without creative labor fall within the protection scope of the application.

[0028] It should be noted that the embodiments in the application and the features in the embodiments can be combined with each other without conflict.

[0029] Specific implementation manner one, see Figure 1 and Figure 2 The preparation method of the porous boron-doped diamond composite thin film temperature sensor according to the present embodiment includes the following steps:

[0030] The transition layer 2 and the intrinsic diamond film 3 are sequentially deposited on the temperature measuring workpiece 1 by using a chemical vapor deposition method, and the periodic mask 4 is arranged; the porous boron-doped diamond film 5 is obtained by selectively growing on the intrinsic diamond film 3, then the intrinsic diamond film 3 is deposited on the porous boron-doped diamond film 5, and the contact electrode 7 and the lead 8 are installed, so that the preparation of the porous boron-doped diamond composite film temperature sensor is completed; the porous boron-doped diamond film 5 has a periodic micro-nano aperture structure.

[0031] In the embodiment, the thermal sensitivity of the boron-doped diamond conductivity and the regulation of the micro-nano porous structure on the phonon transmission are utilized to realize high-sensitivity detection and rapid response to temperature changes; the porous boron-doped diamond film 5 is formed, and the periodic micro-nano aperture structure can cause phonon coherence in the phonon transport process in the boron-doped diamond, weaken the interaction between phonons and electrons, and enhance the transport capacity of electrons, so that the electrical properties and temperature sensitivity of the boron-doped diamond are greatly improved.

[0032] Meanwhile, the thicknesses of the transition layer 2, the intrinsic diamond film 3, the porous boron-doped diamond film 5 and the contact electrode 7 are all microns, the micron-level composite film structure formed above is deposited on the surface of the temperature measuring workpiece, has high structural stability and low preparation cost, can be integrated in large quantities, and does not damage the temperature measuring workpiece; the thickness of the transition layer 2 is 5-200 microns.

[0033] The boron-doped diamond has excellent chemical stability and thermal conductivity, can maintain stable performance in extreme environments such as low temperature, strong corrosion and space radiation, and can be widely used in thermal management systems, electronic devices, biomedicine, aerospace and other fields to provide efficient temperature measurement and monitoring solutions.

[0034] In specific applications, the porous boron-doped diamond composite film temperature sensor prepared by the application can be used as a temperature sensing probe, and the porous boron-doped diamond composite film temperature sensor prepared by the application can be combined with an existing temperature sensing system for application, as shown in Figure 3 The signal acquisition unit in the temperature sensing system acquires the current signal between the two leads 8, and sends the acquired current signal to the signal processing unit in the temperature sensing system to realize conductivity signal calculation and temperature value calculation functions; the measured temperature information is displayed through an external display device such as a display; the conductivity signal calculation and temperature value calculation functions can be realized by using the existing technology.

[0035] Before using the temperature sensor prepared by the application, the boron-doped diamond film 5 needs to be calibrated for current-temperature. The power supply applies a certain voltage to the porous boron-doped diamond film 5 through two contact electrodes 7, a signal acquisition unit is connected in series in the loop formed by the power supply and the prepared temperature sensor, the current passing through the temperature sensor is collected and sent to the signal processing unit, and the signal processing unit can measure the conductivity of the porous boron-doped diamond film 5 after receiving the current signal, and then convert it into a temperature value. The output interface transmits the measured temperature information to an external display device, such as a display, for display; to realize temperature monitoring and control.

[0036] In a specific application, the transition layer is a carbide forming material such as Ti, Cr, Si or an alloy thereof.

[0037] Specific implementation method two, the difference between the preparation method of the porous boron-doped diamond composite film temperature sensor in this embodiment and the specific implementation method one is that the periodic arrangement of the micro-nano scale pore structure in the porous boron-doped diamond film 5 is composed of an array of holes, or is spliced by a plurality of different periodic units, and each periodic unit is composed of an array of holes.

[0038] Specific implementation method three, the difference between the preparation method of the porous boron-doped diamond composite film temperature sensor in this embodiment and the specific implementation method one is that the cross section of the micro-nano scale hole is rectangular, circular or triangular.

[0039] The shape of the cross section of the mask in this preferred embodiment limits the shape of the cross section of the micro-nano scale hole, and the shapes of the two are the same. By forming micro-nano scale holes with different cross sections, different patterns of porous structures formed by the boron-doped diamond film 5 can be formed to meet the needs of different application scenarios.

[0040] Specific implementation method four, the difference between the preparation method of the porous boron-doped diamond composite film temperature sensor in this embodiment and the specific implementation method one is that the porous boron-doped diamond film 5 with a porous structure is obtained by selective growth of conductive boron-doped diamond on the intrinsic diamond film 3.

[0041] Specific implementation method five, the difference between the preparation method of the porous boron-doped diamond composite film temperature sensor in this embodiment and the specific implementation method one or four is that the thickness of the porous boron-doped diamond film 5 with a porous structure is 5 μm-500 μm, and the optimal thickness is 30 μm, the boron-doped concentration in the boron-doped diamond is 10 16 cm -3 -10 19 cm -3 , and the optimal boron-doped concentration is 10 17 cm -3 .

[0042] Specific implementation six, the difference between the porous boron-doped diamond composite film temperature sensor preparation method of the embodiment and the embodiment one or four is that the chemical vapor deposition is magnetron sputtering, electron beam evaporation or metal organic chemical vapor deposition.

[0043] Specific implementation seven, the difference between the porous boron-doped diamond composite film temperature sensor preparation method of the embodiment and the embodiment one or four is that the thickness of the intrinsic diamond film 3 is 5-500 microns, and the optimal thickness is 20 microns.

[0044] Specific implementation eight, the difference between the porous boron-doped diamond composite film temperature sensor preparation method of the embodiment and the embodiment one or four is that if the material of the temperature measuring workpiece 1 is diamond, the transition layer 2 does not need to be deposited.

[0045] Specific implementation nine, the difference between the porous boron-doped diamond composite film temperature sensor preparation method of the embodiment and the embodiment one is that the installation lead 8 is achieved by using conductive silver paste to connect one end of the two leads 8 to the two contact electrodes 7 respectively and curing treatment.

[0046] In specific application, the contact electrode 7 is realized by using transition metal or transition metal alloy.

[0047] Specific implementation ten, a thin film temperature sensor is obtained by using the preparation method of the porous boron-doped diamond composite film temperature sensor according to the embodiment one or two.

[0048] The technical effects of the present application are verified by specific examples as follows:

[0049] Example 1:

[0050] Taking the temperature measuring workpiece as geological drilling as an example, the preparation method of the polycrystalline diamond bit assembled with the porous boron-doped diamond film temperature sensor applied to geological drilling is implemented according to the following steps:

[0051] I. Take a polycrystalline diamond bit, respectively use deionized water, acetone and alcohol ultrasonic cleaning for 15 minutes, and then put it into the hot wire CVD equipment; deposit 10 microns of intrinsic diamond film on the flat surface which does not participate in grinding, and since the material of the polycrystalline diamond bit is diamond, there is no need to prepare a transition layer;

[0052] II. Put the polycrystalline diamond bit with deposited intrinsic diamond film into the magnetron sputtering film system, and deposit a circular aluminum oxide periodic array with a diameter of 5 microns on the above intrinsic diamond film as a mask for growing the boron-doped diamond film containing periodic micropores next;

[0053] III. Introducing boron source into the hot filament CVD equipment, continuing to deposit boron-doped diamond film with a doping concentration of 10 18 cm -3 and a thickness of 30 μm on the deposited intrinsic diamond film with an alumina lattice;

[0054] IV. Turning off the boron source of the CVD equipment, continuing to deposit 30 μm of intrinsic diamond film on the boron-doped diamond film for encapsulation protection;

[0055] V. Depositing contact electrodes on the left and right sides of the intrinsic diamond film using magnetron sputtering;

[0056] VI. Connecting the lead wires to the two electrodes respectively using conductive silver glue and performing curing treatment;

[0057] VII. Connecting the input end of the lead wire to a constant bias power supply, inputting the output current signal at different temperatures into a signal processing device, and calibrating the boron-doped diamond film probe in current-temperature, to obtain a polycrystalline diamond bit equipped with a porous boron-doped diamond film temperature sensor, which can be assembled to the drill rod 9, as shown in the accompanying drawings. Figure 4

[0058] In application, the periodic micro-nano isothermal hole structure on the bit can enhance the temperature equalization capability of the boron-doped diamond and the surrounding environment in an immersion temperature measurement environment such as liquid, such as the geological drilling environment containing cooling water and mud in the present embodiment.

[0059] Alternatively, the periodic micro-nano hole structure on the surface of the boron-doped diamond film is composed of arrayed through holes, and the cross section of each hole can be rectangular, circular or triangular. Further, the periodic micro-nano isothermal hole structure on the surface of the boron-doped diamond film can also be composed of multiple different periodic units, and each periodic unit can be composed of arrayed holes. The specific structures of different periodic units can be different, but they should all have the function of enhancing the temperature equalization of the boron-doped diamond film with the surrounding environment.

[0060] ​The application scenario of the porous boron-doped diamond composite film temperature sensor prepared in the embodiment is a high-temperature, high-pressure, high-abrasion and non-contact temperature measurement inaccessible geological drilling environment. When the boron-doped diamond film is affected by the temperature of the surrounding drilling environment, the phonon state in the boron-doped diamond film changes, especially the phonons with a frequency of less than 10 THz. Since there is a strong interaction between electrons and phonons, the change in the phonon state density will significantly affect the transport ability of electrons in the material, that is, the resistance. In the case of keeping the voltage unchanged, the changed current signal shows a precise response to the temperature. In addition to the fact that the temperature change can be more sensitively detected by increasing the specific surface area of the sensor, the periodic micro-nano temperature hole structure can cause phonon coherence in the process of phonon transport in the boron-doped diamond, reduce the coupling between phonons and electrons, and enhance the transport ability of electrons, thereby greatly increasing the electrical properties of the boron-doped diamond and its temperature sensitivity, achieving the purpose of enhancing the sensing signal of the boron-doped diamond, and further improving the signal-to-noise ratio, sensitivity and measurement accuracy of temperature measurement, realizing real-time in-situ monitoring and control of drilling temperature. The boron-doped diamond film directly grown on the surface of the polycrystalline diamond drill bit has extremely high hardness, extremely high thermal conductivity and acid and alkali corrosion resistance, and is very suitable for harsh downhole working environments, avoiding the problems that infrared temperature measurement cannot be reached in downhole drilling and that thermocouple temperature measurement needs to damage the drilling tool and is inaccurate.

[0061] Embodiment 2:

[0062] The application also provides a temperature control switch device for assembling the porous boron-doped diamond composite film temperature sensor. In the embodiment, the temperature and conductivity dependence of the boron-doped diamond film is utilized, and the boron-doped diamond sensor is connected in parallel with an electronic element.

[0063] The preparation method of the temperature control switch device for the porous boron-doped diamond composite film temperature sensor is implemented according to the following steps:

[0064] I. A temperature measuring workpiece material is taken, ultrasonically cleaned with deionized water, acetone and alcohol for 15 minutes, and then placed in an electron beam coating system to deposit a 50-micron transition layer Cr2. The temperature measuring workpiece is a non-diamond material, so a transition layer needs to be prepared;

[0065] II. The temperature measuring workpiece material with the deposited transition layer is placed in a diamond deposition device (CVD) to deposit a 20-micron intrinsic diamond film on the surface thereof;

[0066] III. The temperature measuring workpiece material with the deposited intrinsic diamond film is placed in an electron beam coating system to deposit a circular aluminum oxide periodic array with a diameter of 5 microns on the above intrinsic diamond film as a mask for growing a boron-doped diamond film containing a periodic micro-hole in the following step;

[0067] Fourth, a boron source is introduced into the CVD equipment to continue depositing a doping concentration of 2×10 on the intrinsic diamond film with the alumina lattice deposited above. 16 cm -3 A boron-doped diamond film with a thickness of 50 μm; optionally, the boron doping concentration can be determined according to the thermal response requirements of the temperature sensor.

[0068] 5. Turn off the boron source of the CVD equipment and continue to deposit a 20μm intrinsic diamond film on the boron-doped diamond film for encapsulation and protection;

[0069] 6. Deposit contact electrodes on both sides of the above-mentioned intrinsic diamond film using magnetron sputtering;

[0070] 7. Connect the leads to the two electrodes using conductive silver paste and cure them. Then, connect the input terminal of lead 8 to the power supply 10 and the signal acquisition unit 11. The boron-doped diamond sensor is connected in series with the heat dissipation device 12. The signal acquisition unit 11 is used to collect data. Figure 5 The current signal in the circuit where the boron-doped diamond sensor is located. In specific applications, the signal acquisition unit 11 can be replaced with an ammeter. Furthermore, such as... Figure 5 As shown, the heat dissipation device 12 and the temperature measuring workpiece material are integrated with the boron-doped diamond temperature sensor, making the structure of each component compact, closely matched, and saving space.

[0071] When the temperature of the electronic component exceeds the set threshold, the thermal resistance of the boron-doped diamond temperature sensor decreases, triggering an increase in the voltage across the heat dissipation device 11, which then starts working to prevent the equipment from overheating and being damaged.

[0072] The porous boron-doped diamond thin-film temperature sensor of this embodiment is used in integrated electronic devices that are encapsulated inside the device and cannot be accessed by non-contact temperature measurement. The temperature control switch device and manufacturing method for assembling the porous boron-doped diamond thin-film temperature sensor provided by this invention have the following advantages:

[0073] High sensitivity: By utilizing the change in conductivity of boron-doped diamond thin films at different temperatures, the sensor can achieve a fast response and realize high-sensitivity detection of temperature changes;

[0074] High precision: The conductivity of boron-doped diamond changes in a stable manner. By measuring and calculating the conductivity changes of boron-doped diamond films, high-precision temperature measurement can be achieved.

[0075] Fast response: Based on the ultra-sensitive temperature response of the active electron concentration in boron-doped diamond, the temperature sensor has a fast response speed and is suitable for applications requiring rapid temperature detection.

[0076] Simple structure: The thin film structure can be directly deposited on the surface of the device to be measured, without occupying too much volume and causing additional damage to the device to be measured. Compared with the damaged assembly method such as thermocouple, it has higher heat transfer precision and speed.

[0077] High stability: Boron-doped diamond has excellent chemical stability and thermal conductivity characteristics, and can maintain stable performance in extremely high temperature, extremely low temperature, strong corrosion and other extreme environments.

[0078] Wide application: The temperature sensor can be widely used in thermal management system, electronic device, transportation, aerospace, biomedicine and other fields, providing efficient temperature measurement and monitoring solutions.

[0079] Although the present application is described herein with reference to particular embodiments, it is to be understood that these examples are merely illustrative of principles and applications of the present application. It should therefore be understood that numerous modifications can be made to the exemplary embodiments and that other arrangements can be devised without departing from the spirit and scope of the present application as defined by the appended claims. It should be understood that the features described in connection with one embodiment can be used in conjunction with other embodiments described herein. It should also be understood that features described in connection with separate embodiments can be used in combination with one another.

Claims

1. A method for fabricating a porous boron-doped diamond composite thin film temperature sensor, characterized in that, The method comprises the following steps: The method comprises the following steps:

2. The method of claim 1, wherein the method further comprises: The method comprises the following steps:

3. The method of claim 1 or 2, wherein the method further comprises: The method comprises the following steps:

4. The method of claim 1, wherein the method further comprises: The method comprises the following steps:

5. The method of claim 1 or 4, wherein the method further comprises: The boron-doped diamond film (5) with the porous structure has a thickness of 5 μm to 500 μm, and a boron concentration in the boron-doped diamond is 10 16 cm -3 ~10 19 cm -3 .

6. The method of claim 1, wherein the method further comprises: The method comprises the following steps:

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10. 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